toContinuousLinearMap_eq_iff_eq_toLinearMap

English

There is an algebra equivalence between endomorphisms and continuous linear endomorphisms for finite-dimensional spaces.

Русский

Существует алгебраическое эквивалентство между эндоморфизмами и непрерывными линейными эндоморфизмами для конечномерных пространств.

LaTeX

$$$\\mathrm{AlgEquiv}(\\mathrm{LinearMap}(E,E), \\mathrm{ContinuousLinearMap}(E,E))$$$

Lean4

theorem toContinuousLinearMap_eq_iff_eq_toLinearMap (f : E →ₗ[𝕜] E) (g : E →L[𝕜] E) :
    f.toContinuousLinearMap = g ↔ f = g.toLinearMap := by simp [ContinuousLinearMap.ext_iff, LinearMap.ext_iff]

Похожие утверждения